Problem: Simplify the following expression: $ k = \dfrac{p + 5}{3} + \dfrac{-10}{7} $
Explanation: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{7}{7}$ $ \dfrac{p + 5}{3} \times \dfrac{7}{7} = \dfrac{7p + 35}{21} $ Multiply the second expression by $\dfrac{3}{3}$ $ \dfrac{-10}{7} \times \dfrac{3}{3} = \dfrac{-30}{21} $ Therefore $ k = \dfrac{7p + 35}{21} + \dfrac{-30}{21} $ Now the expressions have the same denominator we can simply add the numerators: $k = \dfrac{7p + 35 - 30}{21} $ $k = \dfrac{7p + 5}{21}$